Finite Group Databasebeta

← C43×#25585 #24945602

Subgroups — C43×#25585 #24945602

Order 11008.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3505C211yesmaximal, characteristic, complemented
2C43×#2435C211yesmaximal, characteristic, complemented
3C43×#2433C211yesmaximal, characteristic, complemented
4C43×#2408C211yesmaximal, characteristic, complemented
5C43×#2021C214yesmaximal, complemented
6C43×#1996C211yesmaximal, characteristic, complemented
7C43×#1964C211yesmaximal, characteristic, complemented
8C43×#1889C214yesmaximal, complemented
9C4×#99×C43C211yesmaximal, characteristic, complemented
10C23×D4×C43C2211yescharacteristic
11C43×#553—21no—
12C43×#553—22no—
13C43×#552—21no—
14C43×#551—22no—
15C43×#548—21no—
16C43×#546—21no—
17C43×#539—21no—
18C43×#538—21no—
19C43×#534C2212yes—
20C2×#127×C43—21no—
21C43×#529—21no—
22C2×#124×C43—21no—
23C43×#525—21no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×#121×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#120×C43C2214yes—
28C2×#120×C43C2212yes—
29C43×#518C2212yes—
30C2×C4×D4×C43C2211yescharacteristic
31C2×#99×C43C2212yes—
32C2×#99×C43C2214yes—
33C43×#394—21no—
34C43×#394—22no—
35C43×#392—21no—
36C43×#392—22no—
37C43×#390—21no—
38C43×#390—21no—
39C43×#390—21no—
40C43×#380C2211yescharacteristic
41C43×#379C2212yes—
42C43×#379C2214yes—
43C4×C22⋊C4×C43C2211yescharacteristic
44C4×C22⋊C4×C43C2211yescharacteristic
45C43×#342C2212yes—
46C43×#342C2214yes—
47C25×C43C2312yes—
48C2×#41×C43—21no—
49C22×Q8×C43D411yescharacteristic, complemented
50C22×D4×C43—22no—
51C22×D4×C43—24no—
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C22×D4×C43—21no—
58C22×D4×C43—44no—
59C22×D4×C43D411yescharacteristic, complemented
60C22×D4×C43C2311yescharacteristic
61C22×D4×C43C2312yes—
62C23×C4×C43D411yescharacteristic, complemented
63C23×C4×C43C2311yescharacteristic
64#127×C43—44no—
65#126×C43—22no—
66#126×C43—22no—
67#126×C43—22no—
68#125×C43—21no—
69#125×C43—22no—
70#124×C43—21no—
71#124×C43—22no—
72#124×C43—44no—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—22no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—21no—
83C22⋊Q8×C43—21no—
84#121×C43—21no—
85#121×C43—22no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—44no—
93#120×C43—22no—
94#120×C43—22no—
95#120×C43—28no—
96#120×C43—44no—
97#120×C43—44no—
98C4×Q8×C43—21no—
99C4×D4×C43—22no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109#117×C43—21no—
110#117×C43—22no—
111#117×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic, complemented
114C2×C4⋊C4×C43D411yescharacteristic, complemented
115C2×C4⋊C4×C43D411yescharacteristic, complemented
116C2×C4⋊C4×C43D412yescomplemented
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—24no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—24no—
124C2×C22⋊C4×C43D411yescharacteristic, complemented
125C2×C22⋊C4×C43D412yescomplemented
126C2×C22⋊C4×C43C2312yes—
127C2×C22⋊C4×C43C2312yes—
128C2×C22⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43C2312yes—
130C2×C22⋊C4×C43C2312yes—
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43D411yescharacteristic, complemented
134#99×C43—24no—
135#99×C43—44no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—22no—
140C24×C43—22no—
141C24×C43—22no—
142C24×C43—24no—
143C24×C43—24no—
144C24×C43—44no—
145C24×C43—82no—
146C24×C43C2×D412yes—
147C24×C43C2×D411yescharacteristic
148C24×C43C2411yescharacteristic
149#41×C43—82no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—42no—
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—24no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—21no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—24no—
166C2×D4×C43—24no—
167C2×D4×C43—22no—
168C2×D4×C43—48no—
169C2×D4×C43—44no—
170C2×D4×C43—44no—
171C2×D4×C43—44no—
172C2×D4×C43—44no—
173C2×D4×C43—44no—
174C2×D4×C43—48no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—41no—
180C2×D4×C43—41no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—82no—
184C2×D4×C43—84no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C4⋊C4×C43—22no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—42no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—21no—
227C22⋊C4×C43—21no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—21no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—44no—
238C22⋊C4×C43—48no—
239C22⋊C4×C43—48no—
240C22⋊C4×C43—44no—
241C22⋊C4×C43—84no—
242C22⋊C4×C43—82no—
243C22⋊C4×C43#4114yescomplemented
244C42×C43—22no—
245C42×C43—22no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—42no—
249C42×C43—42no—
250C23×C43—24no—
251C23×C43—24no—
252C23×C43—24no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—24no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—42no—
263C23×C43—44no—
264C23×C43—42no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43—44no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—44no—
275C23×C43—44no—
276C23×C43—88no—
277C23×C43—88no—
278C23×C43C22×D411yescharacteristic
279C23×C43C22×D411yescharacteristic
280C23×C43C22×D411yescharacteristic
281C23×C43C2×#4112yes—
282C23×C43H(5,𝔽2)12yes—
283Q8×C43—42no—
284Q8×C43—81no—
285D4×C43—44no—
286D4×C43—44no—
287D4×C43—44no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—42no—
292D4×C43—44no—
293D4×C43—44no—
294D4×C43—42no—
295D4×C43—81no—
296D4×C43—82no—
297D4×C43—82no—
298D4×C43—816no—
299D4×C43—88no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—24no—
312C2×C4×C43—24no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—41no—
320C2×C4×C43—42no—
321C2×C4×C43—41no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—81no—
330C2×C4×C43—82no—
331C2×C4×C43—82no—
332C2×C4×C43#12011yescharacteristic
333C2×C4×C43#12011yescharacteristic
334C2×C4×C43#12011yescharacteristic
335C2×C4×C43#12011yescharacteristic
336#25585C4311yesmaximal, characteristic, direct product factor, Sylow
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—48no—
346C22×C43—44no—
347C22×C43—48no—
348C22×C43—44no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—44no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—81no—
358C22×C43—84no—
359C22×C43—84no—
360C22×C43—82no—
361C22×C43—84no—
362C22×C43—82no—
363C22×C43—82no—
364C22×C43—82no—
365C22×C43C2×#12011yescharacteristic
366C22×C43#53211yescharacteristic
367C22×C43#53511yescharacteristic
368C22×C43#54612yes—
369C22×C43#55012yes—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—21no—
373C4×C43—44no—
374C4×C43—41no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—42no—
378C4×C43—41no—
379C4×C43—42no—
380C4×C43—82no—
381C4×C43—82no—
382C4×C43B(4,𝔽2)12yes—
383#3505C2×C4311yescharacteristic, complemented
384#2435C2×C4311yescharacteristic, complemented
385#2433C2×C4311yescharacteristic, complemented
386#2408C2×C4311yescharacteristic, complemented
387#2021C2×C4314yescomplemented
388#1996C2×C4311yescharacteristic, complemented
389#1964C2×C4311yescharacteristic, complemented
390#1889C2×C4314yescomplemented
391C4×#99C2×C4311yescharacteristic, complemented
392C2×C43—22no—
393C2×C43—21no—
394C2×C43—22no—
395C2×C43—21no—
396C2×C43—84no—
397C2×C43—81no—
398C2×C43—82no—
399C2×C43#243111yescharacteristic
400C2×C43C2×B(4,𝔽2)11yescharacteristic
401C2×C43#302711yescharacteristic
402C23×D4C22×C4311yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C4312yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C4311yescharacteristic
417C2×#121—21no—
418C2×#121C22×C4311yescharacteristic
419C2×#120C22×C4314yes—
420C2×#120C22×C4312yes—
421#518C22×C4312yes—
422C2×C4×D4C22×C4311yescharacteristic
423C2×#99C22×C4312yes—
424C2×#99C22×C4314yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C4311yescharacteristic
433#379C22×C4312yes—
434#379C22×C4314yes—
435C4×C22⋊C4C22×C4311yescharacteristic
436C4×C22⋊C4C22×C4311yescharacteristic
437#342C22×C4312yes—
438#342C22×C4314yes—
439C43#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C4312yes—
441C2×#41—21no—
442C22×Q8D4×C4311yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C4311yescharacteristic, complemented
453C22×D4C23×C4311yescharacteristic
454C22×D4C23×C4312yes—
455C23×C4D4×C4311yescharacteristic, complemented
456C23×C4C23×C4311yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C4311yescharacteristic, complemented
507C2×C4⋊C4D4×C4311yescharacteristic, complemented
508C2×C4⋊C4D4×C4311yescharacteristic, complemented
509C2×C4⋊C4D4×C4312yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C4311yescharacteristic, complemented
518C2×C22⋊C4D4×C4312yescomplemented
519C2×C22⋊C4C23×C4312yes—
520C2×C22⋊C4C23×C4312yes—
521C2×C22⋊C4C23×C4311yescharacteristic
522C2×C22⋊C4C23×C4312yes—
523C2×C22⋊C4C23×C4312yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C4311yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C4312yes—
540C24C2×D4×C4311yescharacteristic
541C24C24×C4311yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C4311yescharacteristic
588C22×C4C2×D4×C4312yes—
589C22×C4C2×D4×C4311yescharacteristic
590C22×C4C2×D4×C4311yescharacteristic
591C22×C4C2×D4×C4311yescharacteristic
592C22×C4C2×D4×C4311yescharacteristic
593C22×C4C2×D4×C4312yes—
594C22×C4C2×D4×C4311yescharacteristic
595C22×C4C2×D4×C4312yes—
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C4314yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C4311yescharacteristic
672C23C22×D4×C4311yescharacteristic
673C23C22×D4×C4311yescharacteristic
674C23C2×#41×C4312yes—
675C23H(5,𝔽2)×C4312yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C4311yescharacteristic
726C2×C4#120×C4311yescharacteristic
727C2×C4#120×C4311yescharacteristic
728C2×C4#120×C4311yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C4311yescharacteristic
758C22C43×#53211yescharacteristic
759C22C43×#53511yescharacteristic
760C22C43×#54612yes—
761C22C43×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C43×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C43×#243111yescharacteristic
783C2C2×C43×B(4,𝔽2)11yescharacteristic
784C2C43×#302711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C43×#3505C2semidirect
2. C43×#2435C2semidirect
3. C43×#2433C2semidirect
4. C43×#2408C2semidirect
5. C43×#2021C2semidirect
6. C43×#1996C2semidirect
7. C43×#1964C2semidirect
8. C43×#1889C2semidirect
9. C4×#99×C43C2semidirect
49. C22×Q8×C43D4semidirect
59. C22×D4×C43D4semidirect
62. C23×C4×C43D4semidirect
113. C2×C4⋊C4×C43D4semidirect
114. C2×C4⋊C4×C43D4semidirect
115. C2×C4⋊C4×C43D4semidirect
116. C2×C4⋊C4×C43D4semidirect
124. C2×C22⋊C4×C43D4semidirect
125. C2×C22⋊C4×C43D4semidirect
133. C2×C42×C43D4semidirect
243. C22⋊C4×C43#41semidirect
336. #25585C43direct (N × H)
383. #3505C2×C43semidirect
384. #2435C2×C43semidirect
385. #2433C2×C43semidirect
386. #2408C2×C43semidirect
387. #2021C2×C43semidirect
388. #1996C2×C43semidirect
389. #1964C2×C43semidirect
390. #1889C2×C43semidirect
391. C4×#99C2×C43semidirect
439. C43#25585direct (N × H)
442. C22×Q8D4×C43semidirect
452. C22×D4D4×C43semidirect
455. C23×C4D4×C43semidirect
506. C2×C4⋊C4D4×C43semidirect
507. C2×C4⋊C4D4×C43semidirect
508. C2×C4⋊C4D4×C43semidirect
509. C2×C4⋊C4D4×C43semidirect
517. C2×C22⋊C4D4×C43semidirect
518. C2×C22⋊C4D4×C43semidirect
526. C2×C42D4×C43semidirect
636. C22⋊C4#41×C43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#35052
C43×#24352
C43×#24332
C43×#24082
C43×#20212
C43×#19962
C43×#19642
C43×#18892
C4×#99×C432
#2558543